Numerical Solution Of The Heat Equation By Cubic B-Spline Collocation Method

Abstract

This work proposes a numerical scheme for heat parabolic problem by implementing a collocation method with a cubic B-spline for a uniform mesh. The key idea of this method is to apply forward finite difference and Crank–Nicolson methods for time and space integration, respectively. The stability of the presented scheme is proved through the Von-Neumann technique. It is shown that it is unconditionally stable. The accuracy of the suggested scheme is computed through the L_2 and L_∞-norms. Numerical experiments are also given and show that it is compatible with the exact solutions.

Keywords

• collocation methods
• cubic b-spline functions
• heat equation